1. Field of the Invention
This invention relates to the field of slicers in communications systems and more particularly to a slicer for associating a received point which falls outside of a signal constellation with a point in the signal constellation.
2. Background of the Related Art
In certain communications systems, each discrete data value used in communications between a transmitter and a receiver is represented by a point in a signal constellation. Each point therefore represents a sequence of binary bits. The signal constellation is comprised of a full set of valid data points, and is a subset of a larger grid of points, the grid being defined by X and Y axes. Grid points outside of the signal constellation do not represent data used in the communications system.
Each signal constellation point maps to X and Y grid coordinates. To transmit the data represented by a point, the X and Y grid coordinates of the point, which typically are represented by digital (binary) numbers, are first modulated and added. The product is converted from a digital number into an analog voltage and analog voltage is transmitted. Typically, a series of points (data values) are consecutively transmitted, such that the analog voltage appears as an analog waveform of varying amplitude.
At the receiver end, the analog voltage representing the point is converted to a digital number and demodulated to obtain the separate X and Y components. These components are used as coordinates to the grid and ideally map to the signal constellation point which was transmitted by the transmitter. To actually obtain the data represented by the received point, the coordinates are used to address a table holding the data corresponding to the point.
During transmission of an analog signal from the transmitter to the receiver, the shape and amplitude of the signal can be altered by extraneous forces, such as noise. Noise-affected voltages transmitted over a transmission medium which are converted to digital X and Y coordinates typically will map to a point on the grid which does not correspond identically to a signal constellation point. A slicer is used to determine which signal constellation point lies closest to the received point. If the received noise-affected coordinates map to a point which is in an area within the bounds of the signal constellation, the slicer will match the received point to the closest signal constellation point.
When received coordinates map to a point which is outside or on a boundary of the area of the signal constellation, the closest signal constellation point is difficult to determine. Various computationally-intensive calculations are usually required to identify the actual closest signal constellation point. These calculations consume a significant quantity of the valuable cycles of any processor performing the calculations.